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Hyers-Ulam stability of Flett’s points. (English) Zbl 1047.39018

Summary: We show that T. M. Flett’s points [A mean value theorem. Math. Gazette 42, 38–39 (1958)] are stable in the sense of Hyers and Ulam.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
39B22 Functional equations for real functions
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References:

[1] Ulam, S. M., A Collection of Mathematical Problems (1968), Interscience: Interscience New York · Zbl 0086.24101
[2] Gruber, P. M., Stability of isometries, Trans. Amer. Math. Soc., 245, 263-277 (1978) · Zbl 0393.41020
[3] Ulam, S. M., Problems in Modern Mathematics (1960), Science Editions, Wiley · Zbl 0137.24201
[4] Hyers, D. H., On the stability of the linear functional equation, (Proc. Nat. Acad. Sci. U.S.A., 27 (1941)), 222-224 · Zbl 0061.26403
[5] Hyers, D. H.; Ulam, S. M., Approximately convex functions, (Proc. Bull. Amer. Math. Soc., 3 (1952)), 821-828 · Zbl 0047.29505
[6] Hyers, D. H.; Isac, G.; Rassias, Th. M., Stability of Functional Equations in Several Variables (1998), Birkhäuser · Zbl 0894.39012
[7] Hyers, D. H.; Ulam, S. M., On the stability of differential expressions, Math. Magazine, 28, 59-64 (1954) · Zbl 0057.09905
[8] Flett, T. M., A mean value theorem, Math. Gazette, 42, 38-39 (1958) · Zbl 0136.04102
[9] Sahoo, P. K.; Riedel, T., Mean Value Theorems and Functional Equations (1998), World Scientific: World Scientific New Jersey · Zbl 0980.39015
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